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A254569 The number of unordered pairs (f,g) of functions from {1..n} to itself such that fg=gf (i.e., f(g(i))=g(f(i)) for all i). 1
1, 7, 84, 1540, 37345, 1145376, 42402871, 1849021504, 93217426857, 5363120671120, 348669188664511, 25418305492373520, 2064813985107357445, 185896884170249831320, 18459391640792004885375, 2012607682674617326564096, 239898601216105901349115537, 31132586664410794285693925664, 4380971763246528510240944123071, 665896706682993760478978112600400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n) = (A181162(n) - n^n)/2 + n^n.

EXAMPLE

The a(2) = 7 pairs of maps [2] -> [2] are:

01: [ 1 1 ] [ 1 1 ]

02: [ 1 1 ] [ 1 2 ]

03: [ 1 2 ] [ 1 2 ]

04: [ 1 2 ] [ 2 1 ]

05: [ 1 2 ] [ 2 2 ]

06: [ 2 1 ] [ 2 1 ]

07: [ 2 2 ] [ 2 2 ]

CROSSREFS

Cf. A181162 (ordered pairs), A254570 (unordered pairs, f and g distinct).

Sequence in context: A034323 A172455 A258174 * A183177 A058795 A027459

Adjacent sequences: A254566 A254567 A254568 * A254570 A254571 A254572

KEYWORD

nonn

AUTHOR

Joerg Arndt, Feb 01 2015

STATUS

approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)